The quarterly payments are called estimated tax payments. You can make the payments jointly or with just your name and Social Security number. Either way you enter the estimated tax payments in your joint tax return, and they get applied to the total tax on your joint return. As long as you file jointly, it doesn't really matter whether you make the payments jointly or in only your name.
To enter the estimated tax payments in TurboTax, in the Search box type "estimated taxes paid" (without the quotes), then click the link that says "Jump to estimated taxes paid." On the page that it takes you to, click the Start button for "Federal estimated taxes for 2022."